Hair is usually a longer, coarser material. In some animals with an outer (hairy) coat and a softer (furry or fluffy) undercoat, the undercoat is what provides insulation and warmth while the longer guard hairs repel water and keep the undercoat dry. We humans have mostly lost the undercoat. However, as a handspinner, I can tell you that the undercoat of animals makes a more soft, warm, comfortable yarn and textile product, such as a sweater that you might want to wear. The guard hairs make a tougher, more durable yarn and textile that you wouldn’t want to wear, but is more suitable for things like rugs.
Some animals, such as certain breeds of sheep, have been bred to promote a softer undercoat as all they have left, just like people only have the hair, because it’s a big, labor-intensive pain to sit there separating out the undercoat from the top coat. That’s what you have to do when the fiber has both mixed in it, as happens with some animals (like camel).